We study the origin of high-redshift , compact , quenched spheroids ( red nuggets ) through the dissipative shrinkage of gaseous discs into compact star-forming systems ( blue nuggets ) .
The discs , fed by cold streams , undergo violent disc instability ( VDI ) that drives gas into the centre ( along with mergers ) .
The inflow is dissipative when its timescale is shorter than the star formation timescale .
This implies a threshold of \sim 0.28 in the cold-to-total mass ratio within the disc radius .
For the typical gas fraction \sim 0.5 at z \sim 2 , this threshold is traced back to a maximum spin parameter of \sim 0.05 , implying that \sim half the star-forming galaxies contract to blue nuggets , while the rest form extended stellar discs .
Thus , the surface density of blue galaxies is expected to be bimodal about \sim 10 ^ { 9 } M _ { \odot } { kpc } ^ { -2 } , slightly increasing with mass .
Blue nuggets are expected to be rare at low z when the gas fraction is low .
The blue nuggets quench to red nuggets by complementary internal and external mechanisms .
Internal quenching by a compact bulge , in a fast mode and especially at high z , may involve starbursts , stellar and AGN feedback , or Q-quenching .
Quenching due to hot-medium haloes above 10 ^ { 12 } M _ { \odot } provides maintenance and a slower mode at low redshift .
These predictions are confirmed in simulations and are consistent with observations at z = 0 - 3 .